document.write( "Question 393696: how would I solve \"%28x-4%29%2F%284-x%29\"? \n" ); document.write( "
Algebra.Com's Answer #279390 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Many students say \"solve\" when they mean \"simplify\".  You say \"solve an\r\n" );
document.write( "equation or inequality\" but when there is no equation or inequality you\r\n" );
document.write( "have only an expression, so you can only say \"simplify\" or \"rewrite\",\r\n" );
document.write( "not \"solve\".  Your problem has no equal sign or inequality sign, so you\r\n" );
document.write( "can only say \"simplify this\":  \r\n" );
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document.write( "x - 4\r\n" );
document.write( "-----\r\n" );
document.write( "4 - x\r\n" );
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document.write( "The numerator is in standard order but the denominator is not.\r\n" );
document.write( "Let's write the denominator in standard order too.\r\n" );
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document.write( " x - 4\r\n" );
document.write( "-------\r\n" );
document.write( "-x + 4\r\n" );
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document.write( "Now the denominator is in the same order as the numerator, that is,\r\n" );
document.write( "a variable term and then a numerical term.\r\n" );
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document.write( "Notice that the coefficient of x in the numerator is 1 and the\r\n" );
document.write( "coefficient of x in the denominator is -1. Let's put\r\n" );
document.write( "those in:\r\n" );
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document.write( " 1x - 4\r\n" );
document.write( "--------\r\n" );
document.write( "-1x + 4\r\n" );
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document.write( "Now you see that you can factor out 1 in the numerator and -1 in\r\n" );
document.write( "the denominator, like this:\r\n" );
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document.write( " 1(x - 4)\r\n" );
document.write( "----------\r\n" );
document.write( "-1(x - 4)\r\n" );
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document.write( "Notice that when I factored out the -1 in the denominator that \r\n" );
document.write( "the +4 because a -4 inside the parentheses on the bottom.\r\n" );
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document.write( "Now the (x - 4)'s will cancel \r\n" );
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document.write( " 1(x - 4)\r\n" );
document.write( "----------\r\n" );
document.write( "-1(x - 4)\r\n" );
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document.write( "and all that's left is\r\n" );
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document.write( "   1\r\n" );
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document.write( "  -1\r\n" );
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document.write( "which is just -1.\r\n" );
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document.write( "So the answer is -1.\r\n" );
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document.write( "--------------------------------------------------\r\n" );
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document.write( "A shortcut rule is to realize that each of these\r\n" );
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document.write( "(A - B) and (B - A)\r\n" );
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document.write( "is -1 times the other.  However this is a dangerous rule to \r\n" );
document.write( "learn unless you learn it very precisely and don't get careless\r\n" );
document.write( "and think (A - B) and (A + B) can be handled by this rule. \r\n" );
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document.write( "However if you knew that rule precisely you could just say\r\n" );
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document.write( "x - 4\r\n" );
document.write( "-----  \r\n" );
document.write( "4 - x\r\n" );
document.write( " \r\n" );
document.write( "and in two steps you'd have \r\n" );
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document.write( "-1\r\n" );
document.write( "x - 4\r\n" );
document.write( "-----\r\n" );
document.write( "4 - x\r\n" );
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document.write( "-1.\r\n" );
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document.write( "Edwin
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